If you want to stay in AVR-land, there's no official board between the Uno and the Mega2560. There are unofficial boards (with good support via hansibul's core) with the ATmega1284p, and I think the ATmega2561 with more pins than the atmega328p but fewer than the 2560.

There are also all the "faster" arduinos like the Zero and other SAM based boards. These are pretty well supported, and can do computations faster, but they're 3.3v (so you need level shifting to interface with 5v stuff) and the library support isn't quite as good.

Word of terminology: "powerful" is ambiguous - most poeple take it to mean processing speed, not number of pins. A mega2560 is actually ever so slightly slower than a 328p, due to differences in certain instructions to support the larger flash address space.